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Fp is constant for each string (That is the even force used to pluck the string), so we can easily see that xp1 > xp2.Since the smaller diameter string stretches more under the same force,the amplitude of its standing wave will be greater.

- Action: You can have a lower action on a guitar, for a same tuning, when using heavier gauge strings. Because of the greater tention in the string, it will occupy less space when vibrating (amplitude) if it was picked with the same force as the lighter string. I will prove this by using Hooke's law later in the artice

- Output: Since a heavier string gauge has more tension, it has more stored energy (Hooke's law F=K.x). This greater energy is directly translated into greater output in an acounstic guitar. In an electric guitar, the output is increased because the thicker strings incur a stronger variation in the magnetic field of the pickups.

- Artificial Harmonics: One of the best ways to explain an artificial harmonic is to quote the Wikipedia article:

"To produce an artificial harmonic, a stringed instrument player holds down a note on the neck with the non-dominant hand, thereby shortening the vibrational length of the string, uses a finger to lightly touch a point on the string that is an integer divisor of its vibrational length, and plucks or bows the side of the string that is closer to the bridge. This technique is used to produce harmonic tones that are otherwise inaccessible on the instrument. To guitar players, one variety of this technique is known as a pinch harmonic.

This technique, like natural harmonics, works by canceling out the fundamental tone and one or more partial tones by deadening their modes of vibration."

Producing an artificial harmonic is a sinch on heavier strings (like a 0.52 tuned to E) because of the increased tension and stored energy. Just try it. If you're currently able to do a pinch harmonic on your lower string, try down tuning it a step and half and try again. Not so easy anymore, is it?